Sounds like you are new to this hobby. There are few things you need to be absolutely aware when you are starting out this hobby. The first thing is called "cycling the tank". Without this, your fish won't live very long in your tank.

Here's an article that explains what a cycling process is:

http://aqadvisor.com/articles/Cycling.php

Then you will have to choose fish based on your tank size. In general smaller species require smaller tanks but this is not always the case.

For smaller tanks (40g or smaller), I would suggest the following combination:

- a group of peaceful tetras (neon tetra, cardinal tetra, etc)
or a group of peaceful barbs (cherry barb, etc)
or a group or peaceful danios (zebra danio, etc)
or a group of peaceful rasboras (harlequin rasbora, etc)
- a group of corydoras catfish
- a center piece fish (e.g. dwarf gourami, honey gourami or german blue rams)

Depending on the size of your tank, you can either hold more or less than what has been suggested here already.

Try using the following stocking calculator:

http://www.aqadvisor.com

This calculator will report:
- your overall bioload % (i.e. how full your tank is)
- your filtration capacity % (i.e. whether your current filter will be sufficient or not)
- water change volume calculator (i.e. how much water do you need to change weekly?)
- compatibility checker (i.e. if your fish species will get along or not)

It will also produce all kind of other warnings as well. As an example, if you choose a species that will outgrow your tank, it will give you this warning too.

Try entering your tank dimension, then hit "Display only suitable species" button. It will narrow down the list from 800+ species down to the ones that will only be suitable to your tank size.

Good luck!

It all depends what size of the tank you have. If you have for example 1.5 gallon tank then the best would be to buy just a Betta which is tropical freshwater fish. Males Bettas are very nice looking fishes while females are not. Also, you cannot place two Bettas in the same, small tank because they would fight (Bettas are agressive). You have to have big tank with some hidden places that they would hide from each other.

Freshwater Betta male:

http://www.ppaquarium.com/..%5Cimages%5CBETTA%20MALE%20BLUE.JPG
http://ebetta.com/wp-content/uploads/2007/10/yellow-indigo-betta-fish.jpg
http://ebetta.com/wp-content/uploads/2007/08/beta-yellow-pearl.jpg
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Also, for freshwater fishes you should have 1.5-30 gallons tank.
For the saltwater fishes the size of the tank should be bigger 30-60 gallons.

In addition, you should know that freshwater fishes are easier to keep and less expensive then saltwater fishes, but in real world saltwater fishes are mush nicer then freshwater.
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saltwater fishes:

http://www.abirdyphotos.com/photogallery/Pictures/Fish/Salt%20Water%20Fish/2004_8880_TwoOppositesSaltWaterAngelFish.jpg
http://www.petstorecaresheets.com/images/caresheetimages/saltfish.jpg
http://www.aquariumtip.info/images/logo.jpg

In addition, you can look at freshwater compatibility chart which I found at petco.com there you can see which fish you can mix with:

http://www.petco.com/assets/livefish/freshwaterchart.html

For more information I would suggest to go to petco or petsmart stores and ask the assistance to help because you can buy any fish for any money ($4-$70) but not enough care can just killed them.

I am not going to do much here, but i will mention a few things. I assume since you are a beginner you will be running a freshwater aquarium. To make sure you have this set up correctly do a search on setting up a freshwater aquarium. Now for your question. Community fish and compatibility. In the references before click on the link. It is actually a compatibility chart. Use that as a guide. It appears fairly accurate. Most freshwater live-bearers are good in a community tank. Just remember that overcrowding will probably cause a littl aggressiveness.